Generating continuous-variable cluster states using optomechanics.

Cluster states are a group of entangled states known for their special properties such as maximum connectivity and high resiliency against noise. They can be a useful resource for measurement-based quantum computing. Here we develop a unique approach to generate a dual-rail continuous-variable cluster state in a hybrid optomechanical system, consisting of cavity modes, mechanical modes, and qubits. Our scheme is based upon local interactions with neighboring modes and can be scalable to a large number of cavity and mechanical modes. We characterize the multipartite entanglement in these states and show that they are robust against cavity and mechanical losses. We also show that the entanglement within the cluster state can be transferred to two distant qubits by manipulating the cluster states via measurement. This system thus can be utilized as a means for long-distance spin entanglement.